## EXAMPLE 3 Looking at Limits of Partial Sums
For each of the following series, find the first five terms in the sequence of partial sums. Which of the series appear to converge?
(a) 0.1+0.01+0.001+0.0001+⋯
(b) 10+20+30+40+⋯
(c) 1−1+1−1+⋯
(a) 0.1+0.01+0.001+0.0001+⋯
(b) 10+20+30+40+⋯
(c) 1−1+1−1+⋯